Once again, it should be noted that the definition of higher order linear homogenous differential equations are analogous to that of first and second order linear homogenous differential equations.

Now recall that if we have a second order linear homogenous differential equation $\frac{d^2y}{dt^2} + p(t)\frac{dy}{dt} + q(t)y = 0$, then if $y = y_1(t)$ and $y = y_2(t)$ are solutions to this differential equation, then any linear combination $y = Cy_1(t) + Dy_2(t)$ is also a solution to this differential equation. The following result extends this to higher order linear homogenous differential equations.